Improved discrepancy bounds for hybrid sequences involving Halton sequences
type: Item
instance of: scholarly article
title: Improved discrepancy bounds for hybrid sequences involving Halton sequences
zbMATH Open document ID: 1270.11078
author: Harald Niederreiter
published in: Acta Arithmetica
publication date: 2012-10-05T00:00:00Z
Mathematics Subject Classification ID: 11K38
Mathematics Subject Classification ID: 11K45
Mathematics Subject Classification ID: 65C05
Mathematics Subject Classification ID: 65C10
zbMATH DE Number: 6090450
zbMATH Keywords: discrepancy
zbMATH Keywords: hybrid sequence
zbMATH Keywords: Halton sequence
zbMATH Keywords: Kronecker sequence
zbMATH Keywords: pseudorandom numbers
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.4064/aa155-1-7
OpenAlex ID: W2312961315
DOI: 10.4064/AA155-1-7
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review text: In this paper the author considers various hybrid sequences in the \(s+t\)-dimensional unit cube, where the \(s\)-dimensional component stems from the Halton sequence. In particular, he mixes the Halton sequences with, Kronecker sequences, explicit nonlinear congruential sequences, digital explicit inversive sequences, or recursive inversive sequences. In all these cases the author provides asymptotic upper bounds for the discrepancy. Moreover he manages to improve several of his former results, e.g. [\textit{H. Niederreiter}, Acta Arith. 138, No. 4, 373--398 (2009; Zbl 1268.11102); Monatsh. Math. 161, No. 2, 193--222 (2010; Zbl 1273.11117)] or [\textit{H. Niederreiter} and \textit{A. Winterhof}, Unif. Distrib. Theory 6, No. 1, 33--56 (2011; Zbl 1338.11074)].
reviewed by: Volker Ziegler
description: scientific article; zbMATH DE number 6090450